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Percent Equations in Geometry

Learn how to solve percent equations in geometry, including finding percentages, ratios, and angles. Practice working with geometric concepts and equations. Homework assigned.

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Percent Equations in Geometry

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  1. Lesson 7:Percent, Equations from Geometry

  2. The Latin word for “by” is per and the Latin word for “hundred” is centum. Thus, the word percent literally means “by the hundred”. The percent equation is exactly the same equation as the fractional part of a number equation, except that the denominator of the fraction is 100. WF x of = is P/100 x of = is

  3. There are two other forms of the percent equation that are often used. P/100 = is/of We call this the ratio form of the percent equation. Rate x of = is In this form the rate is the percent divided by 100. If the percent was 20%, then the rate would be 0.2.

  4. Any of the three percent equations can be used. They are not different equations but are three different forms of the same equation.

  5. There are two types of percent problems. In one type the original quantity is divided into two parts, and the final percent is less than 100. in the second type the original quantity increases, and the final percent is greater than 100. it is helpful to be able to draw diagrams that give us a picture of the problem.

  6. Example: Eighteen is 20 percent of what number? Work the problem and then draw the completed diagram.

  7. Answer: P/100 x of = is 20/100 x WN = 18 WN = 90 100% Of 90 72 is 80% 80% 18 is 20% 20%

  8. Example: Fifteen hundred is what percent of 250? Work the problem and then draw the completed diagram.

  9. Answer: WP/100 x 250 = 1500 WP = 600 percent 100% of 250 600% 1500 is 600%

  10. We can devise problems that let us practice working with geometric concepts and that also let us practice solving equations. Please note that when we write the equations, we do not have to use the degree symbol. If A° + 10° = 14° then A + 10 = 14.

  11. Example: Find x. B (7x + 18)° (6x + 10)° (2x + 2)° A C

  12. Answer: (2x + 2) + (7x + 18) + (6x + 10) = 180 x = 10 Angle A = 22° Angle B = 88° Angle C = 70°

  13. Example: Find x. then find the measure of a small angle and the measure of a large angle. (4x + 33)° (3x)°

  14. Answer: 4x + 33 + 3x = 180 x = 21 Large angle = 117° Small angle = 63°

  15. Example: The measures of angles A, B, C and D are in the ratio of 1:2:4:2. Find the measure of each angle. C° B° D° A°

  16. Answer: x + 2x + 4x + 2x = 180 x = 20 A = 20° B = 40° C = 80° D = 40°

  17. HW: Lesson 7 #1-30

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